Question

Mary Ann solves the inequality −3x≥12 . Justify the steps Mary Ann takes to find the solution set.(1 point) Responses Mary Ann adds −3 to both sides of the inequality and changes the inequality symbol to ≤ to get x≤9. Mary Ann adds negative 3 to both sides of the inequality and changes the inequality symbol to less-than-or-equal-to to get x less-than-or-equal-to 9 . Mary Ann divides both sides of the inequality by −3 and changes the inequality symbol to ≤ to get x≤−4. Mary Ann divides both sides of the inequality by negative 3 and changes the inequality symbol to less-than-or-equal-to to get x less-than-or-equal-to negative 4 . Mary Ann adds −3 to both sides of the inequality to get x≥9. Mary Ann adds negative 3 to both sides of the inequality to get x greater-than-or-equal-to 9 . Mary Ann divides both sides of the inequality by −3 to get x≥−4.

Answer 1

To solve the inequality \(-3x \geq 12\), Mary Ann should follow these steps correctly:

1. **Divide both sides by \(-3\):** When dividing or multiplying both sides of an inequality by a negative number, the direction of the inequality sign must be reversed.

\[
-3x \geq 12
\]
Dividing both sides by \(-3\) gives:
\[
x \leq -4
\]

2. **Change the inequality symbol:** Because we divided by a negative number, the inequality symbol changes from \(\geq\) to \(\leq\).

Thus, the correct response is:

**Mary Ann divides both sides of the inequality by negative 3 and changes the inequality symbol to less-than-or-equal-to to get \(x \leq -4\).**